Finite Group Databasebeta

← #11887999

Subgroups — #11887999

Order 1152.

1158 conjugacy classes of subgroups.

The subgroup lattice has 378 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#556C211yesmaximal, characteristic, complemented
2#10596022C211yesmaximal, characteristic
3#10592792C211yesmaximal, characteristic, complemented
4#10592786C211yesmaximal, characteristic, complemented
5#10592750C212yesmaximal, complemented
6#10592746C212yesmaximal, complemented
7#10592730C211yesmaximal, characteristic, complemented
8C4×#3755C211yesmaximal, characteristic, complemented
9D4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
10#10592701C212yesmaximal, complemented
11#10592695C212yesmaximal, complemented
12#83664—34nomaximal
13C2×#3828C2212yes—
14C32×C4⋊Q8C2211yescharacteristic
15C32×#126—22no—
16C32×#124—21no—
17C32×C22⋊Q8C2212yes—
18C32×C4×Q8—21no—
19C32×C4×Q8C2211yescharacteristic
20C32×C4×D4C2211yescharacteristic
21C32×#117C2212yes—
22C2×#3756C2212yes—
23C2×#3755C2211yescharacteristic
24#64147—21no—
25#64133C2212yes—
26C22×C3⋊(C3⋊C8)C2212yes—
27C4⋊C4×C3⋊D3—21no—
28#64092—22no—
29C4×C4⋊(C3⋊D3)C2211yescharacteristic
30#64078C2211yescharacteristic
31#63662C2211yescharacteristic
32#63657C2212yes—
33#63637C2212yes—
34#63637C2212yes—
35#63637C2212yes—
36#63636C2212yes—
37#63636C2211yescharacteristic
38#63635C2211yescharacteristic
39#63634C2212yes—
40C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
41C4×C3⋊(C3⋊C8)C2211yescharacteristic
42C3×#556D314yescomplemented
43#5551—34no—
44#5093—34no—
45#5087—34no—
46#5051—38no—
47#5047—38no—
48#5031—34no—
49C4×#215—34no—
50D4×C3⋊C8—34no—
51#5002—38no—
52#4996—38no—
53C2×C32×Q8—21no—
54C2×C32×Q8C2311yescharacteristic
55C2×C32×D4D411yescharacteristic
56C22×C32×C4C2312yes—
57C2×#638—22no—
58#3828—24no—
59#3828—42no—
60C2×C4⋊(C3⋊D3)C2311yescharacteristic
61C2×C4×C3⋊D3—21no—
62C2×C4×C3⋊D3—22no—
63C2×#634C2312yes—
64C32×C4⋊C4—22no—
65C32×C4⋊C4—21no—
66C32×C4⋊C4—21no—
67C32×C4⋊C4D411yescharacteristic
68C32×C4⋊C4C2312yes—
69C32×C4⋊C4C2311yescharacteristic
70C32×C22⋊C4—22no—
71C32×C22⋊C4—22no—
72C32×C22⋊C4D412yes—
73C32×C42—22no—
74C32×C42—21no—
75C32×C42C2311yescharacteristic
76#3757—22no—
77#3756—42no—
78#3755—22no—
79#3752—21no—
80C4⋊(C3⋊Dic3)—21no—
81C4⋊(C3⋊Dic3)—21no—
82C4⋊(C3⋊Dic3)C2311yescharacteristic
83#3750—22no—
84C2×C3⋊(C3⋊C8)—42no—
85C2×C3⋊(C3⋊C8)C2311yescharacteristic
86C2×C3⋊(C3⋊C8)C2312yes—
87C2×C3⋊(C3⋊C8)C2311yescharacteristic
88#3302—91noSylow
89C2×#235—38no—
90C3×C4⋊Q8C2×D314yes—
91C3×#126—28no—
92C3×#124—24no—
93C3×C22⋊Q8C2×D318yes—
94C3×C4×Q8—24no—
95C3×C4×Q8C2×D314yes—
96C3×C4×D4C2×D314yes—
97C3×#117C2×D318yes—
98C2×#216—38no—
99C2×#215—34no—
100#938—64no—
101#924—38no—
102C22×C3⋊C8—38no—
103D3×C4⋊C4—64no—
104#883—68no—
105C4×D12—34no—
106#869—34no—
107#835—34no—
108#830—38no—
109#810—38no—
110#810—38no—
111#810—38no—
112#809—34no—
113#809—38no—
114#808—34no—
115#807—38no—
116C4⋊(C3⋊C8)—34no—
117C4×C3⋊C8—34no—
118C23×C32C2×D412yes—
119C22×C3⋊D3—21no—
120C32×Q8—21no—
121C32×Q8—21no—
122C32×Q8—42no—
123C32×D4—22no—
124C2×C32×C4—22no—
125C2×C32×C4—22no—
126C2×C32×C4—21no—
127C2×C32×C4—21no—
128C2×C32×C4—22no—
129C2×C32×C4C2×D412yes—
130C2×C32×C4C2×D411yescharacteristic
131C2×C32×C4C2×D411yescharacteristic
132C2×C32×C4C2411yescharacteristic
133#638—44no—
134C2×C3⋊Dic3—21no—
135C2×C3⋊Dic3—22no—
136C4⋊(C3⋊D3)—21no—
137C4⋊(C3⋊D3)#4112yes—
138C4×C3⋊D3—44no—
139C4×C3⋊D3—42no—
140#634—22no—
141#634—22no—
142C3⋊(C3⋊C8)—21no—
143C3⋊(C3⋊C8)—21no—
144C3⋊(C3⋊C8)—22no—
145#556C3⋊D311yescharacteristic, complemented
146#547—91no—
147#487—91no—
148#485—92no—
149#474—91no—
150#467—92no—
151#462—91no—
152#452—92no—
153C4×SD16—91no—
154C8×D4—91no—
155#416—92no—
156C2×C3×Q8—24no—
157C2×C3×Q8C22×D314yes—
158C2×C3×D4#6714yes—
159C22×C3×C4C22×D318yes—
160C2×#67—68no—
161#235—616no—
162#235—128no—
163C2×D12—34no—
164C2×C4×D3—64no—
165C2×C4×D3—68no—
166C2×Dic6—38no—
167C3×C4⋊C4—28no—
168C3×C4⋊C4—24no—
169C3×C4⋊C4—24no—
170C3×C4⋊C4#6714yes—
171C3×C4⋊C4C22×D318yes—
172C3×C4⋊C4C22×D314yes—
173C3×C22⋊C4—28no—
174C3×C22⋊C4—28no—
175C3×C22⋊C4#6718yes—
176C3×C42—28no—
177C3×C42—24no—
178C3×C42C22×D314yes—
179#217—68no—
180#216—128no—
181#215—68no—
182(C2×D3)⋊C4—64no—
183C4⋊Dic3—34no—
184C4⋊Dic3—64no—
185C4⋊Dic3—64no—
186Dic3⋊C4—68no—
187C2×C3⋊C8—34no—
188C2×C3⋊C8—34no—
189C2×C3⋊C8—38no—
190C2×C3⋊C8—128no—
191C22×C32—22no—
192C22×C32—22no—
193C22×C32—22no—
194C22×C32C22×D411yescharacteristic
195C2×C3⋊D3—22no—
196C2×C3⋊D3—41no—
197C2×C3⋊D3—41no—
198C32×C4—22no—
199C32×C4—21no—
200C32×C4—41no—
201C32×C4—42no—
202C32×C4—41no—
203C32×C4#13512yes—
204C32×C4C2×#4111yescharacteristic
205C32×C4H(5,𝔽2)11yescharacteristic
206C3⋊Dic3—42no—
207C3⋊Dic3—41no—
208C2×#41—92no—
209C2×Q16—92no—
210C2×SD16—91no—
211C22×C8—92no—
212C4⋊Q8—91no—
213C4⋊Q8C2×C3⋊D311yescharacteristic
214#126—22no—
215#124—21no—
216#123—182no—
217C22⋊Q8—92no—
218C22⋊Q8C2×C3⋊D312yes—
219#121—181no—
220C4×Q8—21no—
221C4×Q8C2×C3⋊D311yescharacteristic
222C4×D4—91no—
223C4×D4C2×C3⋊D311yescharacteristic
224#117C2×C3⋊D312yes—
225C2×C4⋊C4—181no—
226#107—92no—
227#106—91no—
228C4⋊C8—91no—
229#103—91no—
230#103—92no—
231#103—92no—
232#103—92no—
233#102—91no—
234#102—92no—
235C22⋊C8—92no—
236C4×C8—91no—
237C23×C3C2×#6718yes—
238C22×D3—64no—
239C3×Q8—24no—
240C3×Q8—24no—
241C3×Q8—48no—
242C3×D4—28no—
243C2×C3×C4—28no—
244C2×C3×C4—28no—
245C2×C3×C4—24no—
246C2×C3×C4—24no—
247C2×C3×C4—28no—
248C2×C3×C4C2×#6718yes—
249C2×C3×C4C2×#6714yes—
250C2×C3×C4C2×#6714yes—
251C2×C3×C4C23×D314yes—
252#67—1216no—
253C2×Dic3—64no—
254C2×Dic3—68no—
255D12—38no—
256D12—64no—
257C4×D3—1216no—
258C4×D3—128no—
259Dic6—68no—
260Dic6—68no—
261C3⋊C8—64no—
262C3⋊C8—64no—
263C3⋊C8—68no—
264C2×C32—42no—
265C2×C32#54611yescharacteristic
266C2×C32C2×#13511yescharacteristic
267C2×C32#57811yescharacteristic
268C3⋊D3—42no—
269#41—184no—
270#41—362no—
271C2×Q8—21no—
272C2×Q8—92no—
273C2×Q8C22×C3⋊D311yescharacteristic
274C2×D4—91no—
275C2×D4—182no—
276C2×D4#63811yescharacteristic
277C22×C4—181no—
278C22×C4—182no—
279C22×C4C22×C3⋊D312yes—
280Q16—362no—
281SD16—182no—
282C2×C8—91no—
283C2×C8—91no—
284C2×C8—92no—
285C2×C8—362no—
286C4⋊C4—22no—
287C4⋊C4—21no—
288C4⋊C4—21no—
289C4⋊C4—91no—
290C4⋊C4—181no—
291C4⋊C4—182no—
292C4⋊C4—181no—
293C4⋊C4#63811yescharacteristic
294C4⋊C4C22×C3⋊D311yescharacteristic
295C4⋊C4C22×C3⋊D312yes—
296C22⋊C4—22no—
297C22⋊C4—22no—
298C22⋊C4—182no—
299C22⋊C4—181no—
300C22⋊C4#63812yes—
301C42—22no—
302C42—21no—
303C42C22×C3⋊D311yescharacteristic
304C22×C3—28no—
305C22×C3—28no—
306C22×C3—28no—
307C22×C3C22×#6714yes—
308C2×D3—68no—
309C2×D3—124no—
310C2×D3—124no—
311C3×C4—28no—
312C3×C4—24no—
313C3×C4—48no—
314C3×C4—44no—
315C3×C4—44no—
316C3×C4#95018yes—
317C3×C4D3×#4114yes—
318C3×C4#100914yes—
319Dic3—124no—
320Dic3—128no—
321C32#330211yescharacteristic, complemented, Sylow
322C23—181no—
323C23C2×#63812yes—
324Q8—21no—
325Q8—21no—
326Q8—42no—
327Q8—182no—
328Q8—182no—
329D4—22no—
330D4—92no—
331D4—181no—
332D4—364no—
333C2×C4—22no—
334C2×C4—22no—
335C2×C4—21no—
336C2×C4—21no—
337C2×C4—22no—
338C2×C4—181no—
339C2×C4—182no—
340C2×C4—364no—
341C2×C4—362no—
342C2×C4C2×#63812yes—
343C2×C4C2×#63811yescharacteristic
344C2×C4C2×#63811yescharacteristic
345C2×C4C23×C3⋊D311yescharacteristic
346C8—181no—
347C8—181no—
348C8—182no—
349C2×C3—48no—
350C2×C3C2×#95014yes—
351C2×C3#582914yes—
352C2×C3#583814yes—
353D3—128no—
354C22—22no—
355C22—22no—
356C22—22no—
357C22—182no—
358C22—361no—
359C22—361no—
360C22C22×#63811yescharacteristic
361C4—22no—
362C4—21no—
363C4—42no—
364C4—41no—
365C4—41no—
366C4—361no—
367C4—362no—
368C4#6415912yes—
369C4#41×C3⋊D311yescharacteristic
370C4#6436611yescharacteristic
371C3#8366414yescomplemented
372C2—42no—
373C2—362no—
374C2C2×#6415911yescharacteristic
375C2#1059630011yescharacteristic
376C2#1059630911yescharacteristic
subgroupG/H
centerC22C22×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#556C2
socleC22×C32C22×D4
prime radical#10596022C2
hypercenter#556C3⋊D3
hypocenterC32#3302
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4×D4 ◁ #556

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C32×#556C2semidirect
3. #10592792C2semidirect
4. #10592786C2semidirect
5. #10592750C2semidirect
6. #10592746C2semidirect
7. #10592730C2semidirect
8. C4×#3755C2semidirect
9. D4×C3⋊(C3⋊C8)C2semidirect
10. #10592701C2semidirect
11. #10592695C2semidirect
42. C3×#556D3semidirect
145. #556C3⋊D3semidirect
321. C32#3302semidirect
371. C3#83664semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C32×#5562
#105960222
#105927922
#105927862
#105927502
#105927462
#105927302
C4×#37552
D4×C3⋊(C3⋊C8)2
#105927012
#105926952
#836643